if vector A+B=2i+6j-2k and A-B=4i+2j-11k. Find magnitude of vector A and B?

Question

Only magnitude of vectors is to be find

Answer 1

Given A+B = 2i+6J-2k ---------> (1)

A-B = 4i+2j-11k -----------> (2)

Add (1)& (2)

A+B = 2i+6J-2k

A-B = 4i+2j-11k

______________

2A = 6i+8j-13k

Divide to each side by 2.

2A/2 = (6i+8j-13k)/2

⇒ A = 3i+4j-13/2k

Substitute A in (2).

3i+4j-13/2k-B = 4i+2j-11k

Add B to each side.

3i+4j-13/2k-B+B = 4i+2j-11k+B

Bring all terms to left side except B.

3i+4j-13/2k-4i-2j+11k = B

⇒ B = -i+2j+9/2k

Now find the magnitude of vectors

magnitude of B = sqrt(1+4+81/4)

= Sqrt(5+81/4)

= sqrt(101/4)

= 5.02

magnitude of A = sqrt(9+16+169/4)

= sqrt(25+169/4)

= sqrt(269/4)

= 8.20

Magnitude of A is 8.20 andmagnitude of b is 5.02